I always assumed (as I am prone to do ) that it was the dust from the cedar shavings that caused issues. I may be wrong.

Cedar chests have been used for centuries to store clothing and bedding; they naturally repel fungus and insects and keep damaging UV rays out. The only potential danger that I am aware of is having the heavy lid come down on a child or a child getting closed in the chest (that happened to me as a child), so check out the hinges that are installed and ensure that they are safety hinges if your daughter is small and will have regular access to the chest.